Question

low temperatures for 5 days this week and last week are shown in the table below. which measures of center or variability are greater than 5 degrees? select three choices. the mean of this weeks temperatures the mean of last weeks temperatures the range of this weeks temperatures the mean absolute deviation of this weeks temperatures the mean absolute deviation of last weeks temperatures

Explanation:

Step1: Calculate the mean of last - week's temperatures

The temperatures for last week are 13, 9, 5, 8, 5. The sum is \(13 + 9+5 + 8+5=40\). The mean \(\bar{x}_1=\frac{40}{5} = 8\).

Step2: Calculate the mean of this - week's temperatures

The temperatures for this week are 4, 10, 6, 9, 6. The sum is \(4 + 10+6 + 9+6=35\). The mean \(\bar{x}_2=\frac{35}{5}=7\).

Step3: Calculate the range of last - week's temperatures

The highest value in last - week's temperatures is 13 and the lowest is 5. The range \(R_1=13 - 5=8\).

Step4: Calculate the range of this - week's temperatures

The highest value in this - week's temperatures is 10 and the lowest is 4. The range \(R_2=10 - 4 = 6\).

Step5: Calculate the mean absolute deviation (MAD) of last - week's temperatures

The deviations from the mean (\(\bar{x}_1 = 8\)) are \(|13 - 8|=5\), \(|9 - 8|=1\), \(|5 - 8|=3\), \(|8 - 8|=0\), \(|5 - 8|=3\). The sum of the absolute deviations is \(5+1 + 3+0+3 = 12\). The MAD of last - week's temperatures \(MAD_1=\frac{12}{5}=2.4\).

Step6: Calculate the mean absolute deviation (MAD) of this - week's temperatures

The deviations from the mean (\(\bar{x}_2 = 7\)) are \(|4 - 7|=3\), \(|10 - 7|=3\), \(|6 - 7|=1\), \(|9 - 7|=2\), \(|6 - 7|=1\). The sum of the absolute deviations is \(3+3 + 1+2+1=10\). The MAD of this - week's temperatures \(MAD_2=\frac{10}{5}=2\).

The range of last week's temperatures (\(R_1 = 8\)) is greater than 5. The mean absolute deviation of last week's temperatures (\(MAD_1=2.4\)) is not greater than 5. The mean absolute deviation of this week's temperatures (\(MAD_2 = 2\)) is not greater than 5. The range of last week's temperatures is greater than 5.

Answer:

• the range of last week's temperatures
• the mean of last week's temperatures (since \(8>5\))
• the mean of this week's temperatures (since \(7>5\))